Objection 1. It would seem that children should follow the condition of their father. Because dominion belongs to those of higher rank. Now in generating the father ranks above the mother. Therefore, etc.
Objection 2. Further, the being of a thing depends on the form more than on the matter. Now in generation the father gives the form, and the mother the matter (De Gener. Animal. ii, 4). Therefore the child should follow the condition of the father rather than of the mother.
Objection 3. Further, a thing should follow that chiefly to which it is most like. Now the son is more like the father than the mother, even as the daughter is more like the mother. Therefore at least the son should follow the father in preference, and the daughter the mother.
Objection 4. Further, in Holy Writ genealogies are not traced through the women but through the men. Therefore the children follow the father rather than the mother.
On the contrary, If a man sows on another's land, the produce belongs to the owner of the land. Now the woman's womb in relation to the seed of man is like the land in relation to the sower. Therefore, etc.
Further, we observe that in animals born from different species the offspring follows the mother rather that the father, wherefore mules born of a mare and an ass are more like mares than those born of a she-ass and a horse. Therefore it should be the same with men.
I answer that, According to civil law (XIX, ff. De statu hom. vii, cap. De rei vendit.) the offspring follows the womb: and this is reasonable since the offspring derives its formal complement from the father, but the substance of the body from the mother. Now slavery is a condition of the body, since a slave is to the master a kind of instrument in working; wherefore children follow the mother in freedom and bondage; whereas in matters pertaining to dignity as proceeding from a thing's form, they follow the father, for instance in honors, franchise, inheritance and so forth. The canons are in agreement with this (cap. Liberi, 32, qu. iv, in gloss.: cap. Inducens, De natis ex libero ventre) as also the law of Moses (Exodus 21).
In some countries, however, where the civil law does not hold, the offspring follows the inferior condition, so that if the father be a slave the children will be slaves although the mother be free; but not if the father gave himself up as a slave after his marriage and without his wife's consent; and the same applies if the case be reversed. And if both be of servile condition and belong to different masters, the children, if several, are divided among the latter, or if one only, the one master will compensate the other in value and will take the child thus born for his slave. However it is incredible that this custom have as much reason in its favor as the decision of the time-honored deliberations of many wise men. Moreover in natural things it is the rule that what is received is in the recipient according to the mode of the recipient and not according to the mode of the giver; wherefore it is reasonable that the seed received by the mother should be drawn to her condition.
Reply to Objection 1. Although the father is a more noble principle than the mother, nevertheless the mother provides the substance of the body, and it is to this that the condition of slavery attaches.
Reply to Objection 2. As regards things pertaining to the specific nature the son is like the father rather than the mother, but in material conditions should be like the mother rather than the father, since a thing has its specific being from its form, but material conditions from matter.
Reply to Objection 3. The son is like the father in respect of the form which is his, and also the father's, complement. Hence the argument is not to the point.
Reply to Objection 4. It is because the son derives honor from his father rather than from his mother that in the genealogies of Scripture, and according to common custom, children are named after their father rather than from their mother. But in matters relating to slavery they follow the mother by preference.
Source: Summa Theologica (New Advent)